{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Attention on MNIST (Saliency and grad-CAM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets build the mnist model and train it for 5 epochs. It should get to about ~99% test accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n",
      "/Users/keisen/.pyenv/versions/3.5.5/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: compiletime version 3.6 of module 'tensorflow.python.framework.fast_tensor_util' does not match runtime version 3.5\n",
      "  return f(*args, **kwds)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading data from https://s3.amazonaws.com/img-datasets/mnist.npz\n",
      "11493376/11490434 [==============================] - 18s 2us/step\n",
      "x_train shape: (60000, 28, 28, 1)\n",
      "60000 train samples\n",
      "10000 test samples\n",
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 180s 3ms/step - loss: 0.2318 - acc: 0.9306 - val_loss: 0.0523 - val_acc: 0.9833\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 174s 3ms/step - loss: 0.0816 - acc: 0.9760 - val_loss: 0.0373 - val_acc: 0.9868\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 176s 3ms/step - loss: 0.0610 - acc: 0.9813 - val_loss: 0.0354 - val_acc: 0.9883\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 170s 3ms/step - loss: 0.0499 - acc: 0.9847 - val_loss: 0.0286 - val_acc: 0.9908\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 187s 3ms/step - loss: 0.0421 - acc: 0.9866 - val_loss: 0.0295 - val_acc: 0.9900\n",
      "Test loss: 0.029462461027854443\n",
      "Test accuracy: 0.99\n"
     ]
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import numpy as np\n",
    "import keras\n",
    "\n",
    "from keras.datasets import mnist\n",
    "from keras.models import Sequential, Model\n",
    "from keras.layers import Dense, Dropout, Flatten, Activation, Input\n",
    "from keras.layers import Conv2D, MaxPooling2D\n",
    "from keras import backend as K\n",
    "\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 5\n",
    "\n",
    "# input image dimensions\n",
    "img_rows, img_cols = 28, 28\n",
    "\n",
    "# the data, shuffled and split between train and test sets\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "\n",
    "if K.image_data_format() == 'channels_first':\n",
    "    x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
    "    x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
    "    input_shape = (1, img_rows, img_cols)\n",
    "else:\n",
    "    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
    "    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
    "    input_shape = (img_rows, img_cols, 1)\n",
    "\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print(x_train.shape[0], 'train samples')\n",
    "print(x_test.shape[0], 'test samples')\n",
    "\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = keras.utils.to_categorical(y_test, num_classes)\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Conv2D(32, kernel_size=(3, 3),\n",
    "                 activation='relu',\n",
    "                 input_shape=input_shape))\n",
    "model.add(Conv2D(64, (3, 3), activation='relu'))\n",
    "model.add(MaxPooling2D(pool_size=(2, 2)))\n",
    "model.add(Dropout(0.25))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(128, activation='relu'))\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(num_classes, activation='softmax', name='preds'))\n",
    "\n",
    "model.compile(loss=keras.losses.categorical_crossentropy,\n",
    "              optimizer=keras.optimizers.Adam(),\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(x_train, y_train,\n",
    "          batch_size=batch_size,\n",
    "          epochs=epochs,\n",
    "          verbose=1,\n",
    "          validation_data=(x_test, y_test))\n",
    "\n",
    "score = model.evaluate(x_test, y_test, verbose=0)\n",
    "print('Test loss:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saliency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize activation over final dense layer outputs, we need to switch the `softmax` activation out for `linear` since gradient of output node will depend on all the other node activations. Doing this in keras is tricky, so we provide `utils.apply_modifications` to modify network parameters and rebuild the graph.\n",
    "\n",
    "If this swapping is not done, the results might be suboptimal. We will start by swapping out 'softmax' for 'linear' and compare what happens if we dont do this at the end."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets pick an input over which we want to show the attention."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x12ee09780>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class_idx = 0\n",
    "indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "\n",
    "# pick some random input from here.\n",
    "idx = indices[0]\n",
    "\n",
    "# Lets sanity check the picked image.\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (18, 6)\n",
    "\n",
    "plt.imshow(x_test[idx][..., 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time for saliency visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x120bdaa20>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vis.visualization import visualize_saliency\n",
    "from vis.utils import utils\n",
    "from keras import activations\n",
    "\n",
    "# Utility to search for layer index by name. \n",
    "# Alternatively we can specify this as -1 since it corresponds to the last layer.\n",
    "layer_idx = utils.find_layer_idx(model, 'preds')\n",
    "\n",
    "# Swap softmax with linear\n",
    "model.layers[layer_idx].activation = activations.linear\n",
    "model = utils.apply_modifications(model)\n",
    "\n",
    "grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, seed_input=x_test[idx])\n",
    "# Plot with 'jet' colormap to visualize as a heatmap.\n",
    "plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To used guided saliency, we need to set `backprop_modifier='guided'`. For rectified saliency or deconv saliency, use `backprop_modifier='relu'`. Lets try these options quickly and see how they compare to vanilla saliency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MGoAOM7uW5EAAdwIYgcqCx6eb2f/l6040jtmrnUZ10xx1fABuTbrrObfljEf8Wvv8CZ/wdz3ODwP/mh3q9W2/6aBg05esDh5wVxA/Kjt0X7AEd1uw6Ymzggf8rRNbHrTdHMRbM+a+mWo58+8CcIGZjUblaXguydGoLOcw38xGAZiPcHkHESmTMPnNbIOZPVm9vR3AKgBDAUwCMLv6sNkATmlWJ0Wk8d7Se36SIwB8DMDjAAab2YZqaCPi6yVFpERqTn6S/QHcDeB8M9vrDbSZGSqfB/TUbhrJTpKdwMu5OisijVNT8pPsjUri325m91Tv3kRySDU+BBmfkJhZh5m1m1k70K8RfRaRBgiTnyQB3AxglZld1S00F8CU6u0pAO5vfPdEpFlYecXuPIAcD+DXAFYAeL1698WovO+/C8B7ATyPSqnPne+YHGrA13N0d6ATi6ZajoZYRmNTP58dmki/6SI//PFXf+nGNwUfp6w5Knt6bKwMhvSGJdIRfvi0qX78mp3ZsZHB0ubT/TCcTQMArvSGEy8OGgfDjUNFlQI7YPZC8ISsCOv8ZrYQlQn3e/Lpt9ItESkPXeEnkiglv0iilPwiiVLyiyRKyS+SKCW/SKJaPHV3bwCHO/HtQXuvdpp3ee9oyWVnSeUF0XBh7/oE4LHHT3Djpx83241/YsX/ZMZuezZYinpWUBKOLn9YG8SHORc5fG6i3/b6YNvboum1o1q+p5nLxQNaoltECqPkF0mUkl8kUUp+kUQp+UUSpeQXSZSSXyRR4Xj+hu6Mww34pvOIqLbqjdn36qZAVGuvzEnqOd6J9Q3aeuPKAWB0EPenz+69JXu8/4A2/9qJrb0GBPteFcSjeRK8Jb6j5140LXhXEPe8/afe7lnt4/l15hdJlJJfJFFKfpFEKflFEqXkF0mUkl8kUUp+kUS1eDz/bvhLZeep1Ufz9kfx6FA44/2PHx+09ev4/e970Y3v2OgPqn/tkuyy7tZ5h7htw+VVFx3nxzdGS3jf6cSiOv2BWosvB535RRKl5BdJlJJfJFFKfpFEKflFEqXkF0mUkl8kUWGdn+RwALcCGIzKAOwOM7uW5AwAXwWwp0h9sZk9mK87UV03qtXn2Xa0HrsTnxeNefdr7Tv6T/SbjwuGZ+9yYtv8prjvueABUS1+RRD3ruvInoegIvp76zqAPGq5yGcXgAvM7EmSAwAsIblntYSrzezK5nVPRJolTH4z2wBgQ/X2dpKrEE97IyIl95be85McAeBjAB6v3nUeyeUkbyF5aEabaSQ7SXYCr+TqrIg0Ts3JT7I/gLsBnG9mLwG4AcAHAIxB5ZXB93tqZ2YdZtZuZu3xXHci0io1JT/J3qgk/u1mdg8AmNkmM9ttZq8DuBHA2OZ1U0QaLUx+kgRwM4BVZnZVt/uHdHvYqQBWNr57ItIstXza/0kAfw9gBcml1fsuBnAGyTGolP/WAvhaU3rYMtEU1N5nnFE5LCojBu0XRdOON7MEGomOmzdMe1POfUsetXzavxBAT4XmnDV9ESmSrvATSZSSXyRRSn6RRCn5RRKl5BdJlJJfJFEtnrq7zF4N4l4tPppyPDrMUXtvWGy0fW+8by2ivkXb17DbstKZXyRRSn6RRCn5RRKl5BdJlJJfJFFKfpFEKflFEkUza93OyBcBPN/trkEAtrSsA29NWftW1n4B6lu9Gtm395nZYbU8sKXJv9/Oyc7K3H7lU9a+lbVfgPpWr6L6ppf9IolS8oskqujk7yh4/56y9q2s/QLUt3oV0rdC3/OLSHGKPvOLSEGU/CKJKiT5SZ5I8ncku0heVEQfspBcS3IFyaWV9QUL7cstJDeTXNntvoEkHya5uvq9xzUSC+rbDJLrq8duKcmTC+rbcJK/Ivk0yadIfqN6f6HHzulXIcet5e/5SR4E4PcATgCwDsATAM4ws6db2pEMJNcCaDezwi8IIfnXAHYAuNXMPlq9798BbDWzmdV/nIea2YUl6dsMADuKXra9uprUkO7LygM4BcBUFHjsnH6djgKOWxFn/rEAusxsjZn9GcAdACYV0I/SM7NHsf9yPJMAzK7eno3Kk6flMvpWCma2wcyerN7eDmDPsvKFHjunX4UoIvmHAvhjt5/XocAD0AMD8AuSS0hOK7ozPRhsZhuqtzcCGFxkZ3oQLtveSvssK1+aY1fPcveNpg/89jfezI4FcBKAc6svb0vJKu/ZylSrrWnZ9lbpYVn5NxR57Opd7r7Rikj+9QCGd/t5GOKVLFvGzNZXv28GcC/Kt/T4pj0rJFe/by64P28o07LtPS0rjxIcuzItd19E8j8BYBTJI0i+E8BkAHML6Md+SParfhADkv0AfAblW3p8LoAp1dtTANxfYF/2UpZl27OWlUfBx650y92bWcu/AJyMyif+zwL4dhF9yOjX+wEsq349VXTfAMxB5WXga6h8NnIWgHcBmA9gNYB5AAaWqG8/AbACwHJUEm1IQX0bj8pL+uUAlla/Ti762Dn9KuS46fJekUTpAz+RRCn5RRKl5BdJlJJfJFFKfpFEKflFEqXkF0nU/wO/TuR9Y+qbnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for modifier in ['guided', 'relu']:\n",
    "    grads = visualize_saliency(model, layer_idx, filter_indices=class_idx,\n",
    "                               seed_input=x_test[idx], backprop_modifier=modifier)\n",
    "    plt.figure()\n",
    "    plt.title(modifier)\n",
    "    plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both of them look a lot better than vanilla saliency! This in inline with observation in the paper.\n",
    "\n",
    "We can also visualize negative gradients to see the parts of the image that contribute negatively to the output by using `grad_modifier='negate'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x132709dd8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, seed_input=x_test[idx], \n",
    "                           backprop_modifier='guided', grad_modifier='negate')\n",
    "plt.imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets try all the classes and show original inputs and their heatmaps side by side. We cannot overlay the heatmap on original image since its grayscale.\n",
    "\n",
    "We will also compare the outputs of guided and rectified or deconv saliency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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59+zU0bfHi9uxiA0ucYZFCmEe63x4l5BaY6YzTF1PbaZQ2PJsf5+HA220S+S1hlQu7BLtEw+xyoBX1/ApA1gl4J8rzsgLBAMat2kLNQz7ysftEvUB1V2o/ZqwHN8z3BnfaolXvJ/yJF8hVUKUV5vvQ0v4SH3FO/XEpXtglVU+k5oBduz68enKMRPC4VW+f2Swv56Npt6Hm2h+fM2poPNoHK9jukNlwlVYT1MWqrW+wrzj78mDxqlPqZF03vNUH+pKzpHO6pn0oBK6QqFQFAhalNBF5A+we328b4wZ7Wj9YMWyEtif/IuMMTty183msf/1N1s+qRESN9n0upf3uY2owYXxmi02x2uvxUHK2Y/c4DVThVpsQVd0w2lyNoBs8pclWi+lsRRLUlxkLyJpL7JlkuQzm6S5Pk5SqaP0umucW+Oj5PrFRs8+TgKdS7StZKwqccaqBG+U6YcpS92HxhxvLGn+HdZ97xAAVwNoDW/jVkDMyzhjI0tyzpA2kHYSGu/Kh8hoXMvP7Q3ELe1wT0ucOm+ITdBxNsI1x6t0kU3ecmI5H0lMxmHPMx5neyjlsJdyyylSdKIT0SkhV7SLEQCs82OJDe3u3AomkROBt6Munk8ncDrjpM1dHfx4KCEa1/39ea/ezN9NKhJ6BSLXhQjTATxjjDkawDPuf0UGOBJDcWLSjr8AlL9Zwhgkpx0EoLzNEpS37REtTujGmH+iqf/MBQDuc/X7AFyY5X4dNOgrA9AFXRuTlb9ZwVDEBG4ob7MC5W17RKZG0cONMVtcfSuSw7raJeq+H3YxevEHVtXSu1NQsyzdG/x2V820/undP1yOPCED/sYlOGLE5VieQPVE0/MmO7XGOLr9QkpSVuxy0HP6+ducqoU3Nn6IjFmDnZ97Ne0aNZI22l3nDYScr9urjprzPfeGpbjIzCbIcOwyfz3qY+rcR47KdcZgVi/N8YYynhhLqO6jOnlXm6KY80ZSPeHK5hKZ5dT/PEPexkU5J0J1q8+0RaqjseSHvtWV5bSZefk3bdmH1Fl1oYpiN7b3sPHYtV9Eqh3QeF/l1IUj6d48JNZ4g/X3iOjf99FEI8eCKMYjgWyg1UZRY4yB3f8sFiJypYhUiUhVPfa29nYHHQ7EX+Yt8FEb96zjI52xq/xND+nxNp9ZMgsLmU7o74nIEQDgyvebO9EYc7cxptQYU9oFHd01sM2QEn+Zt9Y4pUgBGY1d5W9KyJC3hzZ3miJNZKpyeQw2K80sV/49az3KEWq/EIQFVrV4XFoZfE9HPJo3VYtHlvgbtx0afzzs31zd6DwAu50aYeE36Tyy+m911v6SsAS9aKNVoc6Xj8N5nE4g8j8vCTTeMDoKU+cc3uzREAe/qS6rWZod2jkeu6yGWR5DZ9WCV7nw/mSspjk0hua1GLwdH9/Hv0fyZ09S6WS+AXEKyAJv3VZ9SX7Z/nchbJadpGXycQ7V3MbxoY5UKkXkYeSngGLik/fA4tfBvPN+6CV0OCm/vb8WxRUUO3VidQi8+MqgRVH9eXH574vLQps9fq7itAKpIRW3xQdhvev7i0gNgBtgX9h8EbkcwCYkZXRXpIPV5iXswDbUYy9eME8Adj9y5W9W8CCAtwB8DJfdUXmbNTwCq/f1vO0EKG/zjhYndGPMd5o5dGaW+5IT7HvaGsyWjuTkW/bn+YSlIfXlsde8FdVz5XMeh+PllKT/F5sFtcaYD9Aq/sYlivI0ThiVoLrXY55PNCfdlJIRp4p2VlllJfOhJ6yLSJFkPp0k7FlkAI2iU0lyWsa7tXhfYtopJkrUxdIl6129IbfxLkY/aHTejCzwFjiw8ZntgHxv/y7iNpbm67DxzEWVFn07kPwmWmxcTVp1ecNhXCrZxvdqjHSiR7/V6P+7YUxdFnjrpXHiQ1GZLcfQaVupHqUX5pWKjzimVWgDrWrqvBhOaZzr3Lu57axAA0n1/lpVLxKNkswVuT430DVPdam+rw9agecrvhTV+zXYMb29ii55alLodFrQSFGFQqEoEOiErlAoFAWCDpmcqyUUDSuJ6jcO/wsAoC8ZQlc478mhNwblyv4declckCPEJbOKW95zwiCn1pgSdoPCble/Nyzfi+uCKqWoyO6es0nIQjXH1SeTYehiWp77XNOzKWd0kgHM07nvfsNgVlfEubp1iaFlCwahTwf6bLhfrH7x6iB+VsfzsyhJWoIOVztVF6dOqHDlQl6Ws6raX4AN3nG74sSBn6stE3btRTDmuvsOJzXfLFdy9xZQPRpqPyOi98MvIRrvBVDhynKi+bGXCKQi+h4a/LU4RmJjqJY6o+1WUsP4S7FKhd7H9iJf5wRtcTEjqUEldIVCoSgQFKSE/rn54Zf4xK5Nf7O+84zNSzrilZfbrE+5B+/64p+/Fx33BkU2oJEkMNDt8DKPDtdWukpZRNozjo77251KtMleMgwS3rEPBnfktTOcUbaYEy2RlIO/uTIuupF3MYrbLYjdnrMdEWnonnHpib30zvdlidDvcsOfnJPMOUfcmGAM/pGxUuudL5LEt9BH3bLhLs4tsbmo2UZpapOOs3tk3O5QTGu6R2p24K5bTamHJzs+TWx6toWXbtm47iT0ZRTVOY78EWc7Z4RLwm5PITUxPVMDfxAlruTviiJylzk+9af7+D6PD6R+Y8I4PaWz/V7+0Zdcg+vY6JoeVEJXKBSKAoFO6AqFQlEgKBiVy45LQ/KtGYc33fD50kRYoh57rV3KtqW/ee7RgLD8i9s9x9M4aRMlO9rq1R5huXia+RQAsPQVasK+wCWuXEZ+t97/d3Dwrx9Fepy15a5PbPSq5vzS3leY1RXekJggGvvT+47wZsjpb7CbPlpS6/DS3BlIi8JzX1Jvc8fPuyzkju9SWxbVX/dZOAMJGOuM0hxdu5ANzAlXskolLjqV4dU0m5s5z6ti+Jp8LmCTl2WKQxBUUv66iXC4zqlcOAlcHcU2DHZG9z7BYH/L6h8DAI7B1yLahbU/D22qylyFx4n/RjjeIS6//TeIxt+Ya8cqSK9OmxUip7dHRn7gH5ERnSKrIwNx+kZ+ldAVCoWiQKATukKhUBQIOrzKpWjQkQCAL/8k+N3Gbfi89PVgwR+xo5C8WzzYC8ODw8i9hwKFP/ekZEe7XS7okuB9chn+CABYOiakRTBzr4zqcr1PIkReGD7v0IRAeqQX72zjtqirZj9p3iLNL7nZG8epV/xG1kByAqWHvKqFfbP9c+Y0/3cMWC0xqOnhCaH6ulcl0bPsm9I7qsss1/cGCvNf4p+HQ9LZLzrhyjjVChD4wX3zagf2cimhuucvq7m8qsCrlVoTAxCXD53e/54VrkzQcXrXNY4/xWHnr9Uu5/g0+W1EM5uDWqjPZ2za9p1zabewPatdhafFMqp7PpNqrySkZThj47MAgB/gzxFtwhNuA/WpPUKbkCkDuHCCLRcSrcGrZFTlolAoFActOryEvva6IQCARwc+Hnv89NX/A0AwhAKFZgz12I9gzPFSYlzEGUnGu/9KdJeobHSgXOkiQG9AkMrPvyoYMAdc9TYAYNvpR4VG5zQqAWARS+PeWErJucawlOTKdbdQGycNzqLIS44U9Aa1niTB73ZSHTJPdJQZ2Oeb/eKdn3FZoKz8qn3ufS8HyfHWusnhhK+76GbmzypOWuYR55/Pxj5Of+wlX9pFyqcqnhf4e+z3gtS/9i1rYMRtZPic6yV8HzfQmq9qD8J4iPNvd4bksyjieDG3t0b3wetD/+eJlfhvIGPt1iPD6men+BUB8/OTRiWQbIj3fKbv6uJQfVa+aEsOC3WLnp6rtkWkbx0SBu/j+62BdftZtGKq9Es2NpSmBpXQFQqFokCgE7pCoVAUCDq8ymXFN37tavHb2/W+2vpSNxRU8q04dEJQtXiDFS9b/TKSjGWDy0O9xvn1Lgxhx2ONVWVcQW1mbKKN3Eud0aaW/dCd6qYPJZxK2j3naVeSIfR6OuyjuGdPCzSfV20RnTebQrKLrNF12K7XItIG8Sf/O3KHlvKHx3xelGhr5yLrZ/4enTZNglH6z8bGi39/BumXVpXZsn8goYQSSPV0dc4XPp3qkY90eaAlmnZz7V3BAPqrq64GADTcGTZSnzbXvx/f+db4oXPiMz9OSVXm3i9o6GExJ7Oy76HmtOAEcIZ5AwBQ/rtwlgg5so9zDgEL48LsmzNG+nODwfbs/xM2ZXpq4AW2UlYemoyx42J3z6UR6b6k+IQDTcHHHuBYPFRCVygUigJBKlvQDQHwJ9hQNwPgbmPMb0SkH4CHYf2bEgAuMsYUuhicVewxH+M1vIx92ANAMMjtmai8zRbqYP0EP4CTIA8DlL/ZwbsApgDYAMtba81W3uYXqahcGgBcY4xZKSK9AKwQkadhv5RnjDGzRGQ67MJu2gGukxfUH24t2132xfgEN4P92+xusGbv3ogm3YJKp/OA/k3bDLCx2Ouv6XrAa5v9YWn62f/5Kkaa03DIR13RYOqxHM8AVsEwHWnzNs6Xl5/ZL2EprLmGwqenOA8CUmUsecumSxhcSZnveCkfJekjP3SfGoDVI0m5np3ZfzA5X++hw67dJRvviUh/XmO9bMpGB//ffTceGdWXumX1BmFPi+sAbAFwlLvnxwDGHyYio5DTscufFHnlPOreO6mX/tn5ywCAfYbUhRK8tX74wR9shdnnfaBryUuolpbm461f9NnPBVXAOxgS1dfeZFUpP//Ff0a0fcfYMfsrCWkJlpuQpfAxty3hzBNvpn7cCKs2uxp23F2N7PDWq8jID73BqbMm83n3Ud15OS0LnlHP/tzeUirD5vBJaqrIGYnjHXwMBKvP+H06VczkkGLgDXIq/2SifcfFpaHF383ZAIBvvhc8yj4d+N90TU8/mWhexZn0EaWEFlUuxpgtxpiVrr4L1r9oEIALELh6H5I1XIoU0K1TDxza2Y6yIumCHla31hXK2yzhCIRgmR6AnXl07GYFvYHoh6I77LBV3uYbYoxp+Sx/skgJgH/Ceiu/bYzp4+gCYIf/vzkcKv3MKZLdvaUfesf+2sVFh2aKL/3L7otd+1749e47IEi2L530QFbuM+p+K3IMu3YpPjEfoQqV2ItP/gVgWLq8FTnKAFPdf94Hmfyysd6VzSVg8r7KLPk4Z/JJowJpLvkvT/D+y9SkwSeKIsNPCUWkJmI6T77AU4w1bM5+kRIpTXAlBZy+f0O4/l24CgDwyw+C1Fnf368qvChWA+CMfQAGIIOxKzLIWGkUCBJcCZ3hDdHN5JsfMy25O0Bkl1z6rZDx7LQXV4XjYz1jaTUzsMyWnBucrzlrY1PivGAsNK9aKfKVWwJtBaxI+cMXHwxNyPX92859O1EX+jFCvKG2F+yYOg9AfW9kxNuhJlhuXZTkcPI597ERj95DrfihPe95IVDh2kwIpAs597l3IOD4Ff/uyK+/Dxmc63yFBzwNSp/zfAFv4O0d5nlccNyAW0XPpW9skms/nF5CtawwxpDsH4+UjaIi0hPAIwCmGGOS9v8y9lch9pdBRK4UkSoRqarH3rhTDno0mAa8iqU4xuorPuVjqfIW2N0GPe2o+AjAjwHgnUzHrr2Goik+gtWlD0TmvNWxmy2kNKGLSBfYyfx+Y4xX+rwnIke440cgOSwugjHmbmNMqTGmtEszroUHM8z+/XgVSzEQR+EwiXTeafMW6NlGPe5oqIedzM8HgoyVAX8PaYvOdjA0wE7m54EkUB27eUSLKhe3bLoPwHZjzBSi/18AH5Dxo58x5toDXSsXKpdP/ssu558ZvaCFM7OPj82+qF5vPm1y/NxXJ0T1nauaGlIHvlCPN1+dj26bP8QxYpfdi82CFQCeQ5q8TV62+qU++7F6NUHjPNYeLry7iJIIlbiSl/ecFMsb+BIcpu8aDQ9Ji3iLtWsvmAEAuPWJG8Ilz1sf1d+ZN8JWaP6Uo+wYHXDS2xFtm7wRTpjsElXN4aXuSljh8AnYyWYygNNXGGNKMxm7IkNM2ITYC6Jxm0CzjzHxuk+5LdnnfqqlXWuCoXwXtb/zd87YPJfaOD/ywfcEnn0XQQU4EfcCAO6ll3bLX8qjernbT5rTbJ25x8p1PT4KY7jTCzQvXOjfL4+n9QAehB0QVwH4CYxZL5nx9nOq+zCvAAAIt0lEQVQGuNX95433ZGiPxu5qonHsv1OfjKY2a5zKbTbFQ/BGzfNc0qwktaP/biip3TiKofBdK6Emi2hRUu3eXS355J/qVZCU/5/TDYx0udV5n4E1vlxPxBEpqVxS8XL5NwDfB7BaRLyC7zrYvbjni8jlADYheetxRQr4cEcC729eiZ7ojWXGB9ygN5S3WcIG2ECmYXC/SqNE5Fwof7OAjQBWwLqETgZQA+Vt/tHihG6MWYLmw8CyK25ngO5fs0ag424OPk2mhafqNdIaDVsybh73wmXhmm83XXIPW0C6v+Wrmxzvi/WxdcZZMj7p/8VmwU5jzAdIm7dd0DRda4Lq3ojE50wIVb/q3U2JtKqt8eaMac9GpFKsiOq3LnZSdgVHgjpJtTqch8pgWHrpAnfuuHC85rZwXKbalL1YGPr2/klW8rkAwRVv20RKH1sSdTjQilzEZcOXqG8Xv26MedL9kyZ/ixCkuQMlP+P0uST91TlD2m2cSrgMAHDX3pERZVcdSfiTvYGTpNE11tBdszVIkT0eD0mc+jit0q3yg4h26+CwGoossUvKI8qj3eyuPg90+244bTRJ6Nc7Y+PMhwMNQ2Dnbj+u/h+M2Zwhb/sC8EbQClsUU7TmHi+h8+pnJNVdH9bw+3DjeBHtLsRNonfDqYf9t0Fui6zer3VlUr43ijQd7tc9h9HxmBVxf+rTOvfu1v226Xlx6ZdbgEaKKhQKRYFAJ3SFQqEoEKTlh95a5MIoWmhYbBakZPxojGSjnV/2c+Toh42OAckGIe9nP5RoZbaYSYal69kzzRmeisnP3MfxLKLwz4nFoe7UYVc+/puIdBipLmZ2cdGIDXSfCudBURdIbGhFjW/PS27/7Lxx9IyMeAs0x9+45GfN7ZDkDKjDQ5RhFHXrd4tKujaAIrd5NLtcl7jyUaIxLxz/B9wQDMi7dgYvkj2T3DtnXjptZb9zgnpg+yRa7nuNT5Lxu/Fz3g1j3s0oQ5dIqYksliWOyAnFZrqyhnO4s1rDG6d5c2cfXsu7YXGffRTmJKL5cc7vldVMTlWyKviUDz4hqFKPxLsAgOW//0pEKx5v1bt7FtC3NpGN915l8z2irWxUAqmOXZXQFQqFokCgE7pCoVAUCDp8PnRFHHzoP6tU4jwz2KncLU2nU4jyMley73RSCLOr76kMpOoyW84mNQurDNzK+u4rftq02wDQ4MOzlwfa1Am2rH268dkOPlEVq5O8+qA1mxczOPlZ3EbLni9xni8EDkfwucm3hhzokQ8yENQPy0j9NNjdZxmdV0Z151i87cSj4o9X+ntSGPwiq37YnuRFwo285xOPJ97iDmidbLgFwE22mnCqlEl8fZ/Cgj0g2dXEq9XKieZVLvcTjX3BvZ8+5+33/uGsmgneVF2cl0s9aUxqZgZvo5oFXjcVVC57Jjp12hjuG3tj+ZQQN9Fxrybi8ZwaVEJXKBSKAoFK6AWD/QiGTw+WcuJe9fqmx2fxNVzCrtFk61rDuVz9htGUbGiPS6DEhjqW9kqdRMMC1kCqF7skRXvIf7fW+2OT7zko9W8U2UcpZSPJPG4noUxgYq7FPsaevw0xNCB6F8sqAmmZ5xtLvhTPsNVL/cRzLx0u2URtWJLz96SozlU8DjzjuU3cioMjMRtL4wzPk6aR0qmDd9vyhk3mo+8L84kTXHn/b17BeUMpGxs5VsQbWMlIHWvYDuJ4vU8YxqnGSqgeSf1s9HSrilWcGGxCqDZ4gzi/D28oTX/sqoSuUCgUBQKd0BUKhaJAoCqXgwZx/tFxS3FegjoD3xpWwySo7p3OeSnrhxQbT8kXvMovn/nel1LdLzN5+e99hrkfcc+TLQNoqqiPqfPSuSHmOH9yL8acx88Vp8ZpfAxI5ovnwepmjvv+xX36rAfjZ8s1X1md5dUqcX7m/BysEvL84Tb++bnNWVT36SrYz9zznpOQUZi+992vI8N3ooLO9Xzi3Yf+5koeF/Op3iXmuDdOH0jVFQ+V0BUKhaJAoBJ6QSMdo4qXOsqzdO90pIt7s3TPbBlAW4PmIkU9qls4zjjQ8zR3rL6F4y1FtKbbj2yAXULj0junyrPmUkN7LG7huMfKZuotwT9D3H0yfV/pQSV0hUKhKBDohK5QKBQFgjZNziUi22A3Iaxt6dwOhP7I7vMMNcYMSLeR8jYlZMRbQPmbApS3ycjL2G3TCR0ARKQq04x37RHt6XnaU1+ygfb2PO2tP61Fe3qe9tSXbCBfz6MqF4VCoSgQ6ISuUCgUBYJ8TOh35+GeuUR7ep721JdsoL09T3vrT2vRnp6nPfUlG8jL87S5Dl2hUCgUuYGqXBQKhaJA0KYTuoicIyJviEi1iExvuUX7gogMEZHnROR1EXlNRH7q6P1E5GkRWe/Kvnnom/I2d31T3ua2f8rfbMEY0yZ/ADoDeAvAMABdAbwCYFRb3T9Lz3AEgC+4ei8AbwIYBeBWANMdfTqAW9q4X8pb5W2H463yN/t/bSmhnwyg2hizwRizD8BDAC5ow/u3GsaYLcaYla6+C3ZHhUGwz3GfO+0+ABe2cdeUt7mD8ja3UP5mEW05oQ8C8A79X4PkHKkdCiJSAuBE2A0XDzfGbHGHtiLk+2wrKG9zB+VtbqH8zSLUKJoBRKQn7B5oU4wxSfu+Gbu+UtehDKG8zR2Ut7lFe+BvW07omwEMof8Ho+V8l+0OItIF9qXdb4z5qyO/JyJHuONHAHi/jbulvM0dlLe5hfI3i2jLCf1lAEeLyGdFpCuAiwE81ob3bzVERAD8HsBaY8ztdOgxhG13LgXw9zbumvI2d1De5hbK32yija3B58JagN8C8It8WqYz7P9Y2GXTqwBWub9zAXwGwDMA1sNmt++Xh74pb5W3HY63yt/s/mmkqEKhUBQI1CiqUCgUBQKd0BUKhaJAoBO6QqFQFAh0QlcoFIoCgU7oCoVCUSDQCV2hUCgKBDqhKxQKRYFAJ3SFQqEoEPx/FEmqF2qDyiQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DvOC2LOOyDb6fjiWZvz67YdJDLXRFUZQyoV0LXUTuhp0r+KExZqST9YfNEaqGjUScYYz5ONU1csVtV9r8tl8eFP4O7bLMWhwf7x8sji4HhZytm0bav7q3DAlBtCc22yjSyT02oS0+N1uj9vNbwl/ymm7OKqFrDj/TBg73CTGYtHjNLMI6rEYXdMWRcjyAbPVr0DqIwv93VkEVpRhOogDcTKu/x8YMiUSP4W7XogJHfMd6e47pHXQvw9017z8tkn39e3PprKcBAH/7NU0/nUyzQnvV2i2nMs5wlnm3YKElVEpd7kupJs/gfAR2CmxP+FXls++7PBPXw4FDvyh7+Ny4KDQHiZ+FSPpffJtrBCuvb9MFUXtoN/tdHCVBf5OMXX+55kv1kezQTyjF0A0U7ugZLNMf9qqL2gO/YIOJo5eF4dm8PVyqKsehE2YWx80UfQzAG8iJbleAquXa31SXOdQ3vR4vr6WTDqe2G2E08QjOfabLQ9/8aE4o6fx2i03pvdaEgPNv/jDZNqKy0AgF0gDA334kyWZQ2wc+T98ryKa631PVrXQgpfRGF20gGUe0MyMdC70OCcWJAQCTADxjjBkB4Bn3fyULdscwHNL6han6zQmHIDHFBoDqNkeMguq29Gj3hW6M+W+0LiZxCoB7XfteRJ47JVN2kYGoRJdkseo3J+yFmJXiVbc5YRhUt6VHtkHR3Ywxq117DRKrK+WNnrOed9vW+/q0FgEAfje4BgAw5ajqcOyzNnn0ppq2hzYVn4fAS89XVkftXf/bBvwO7EL57g3trcCTEVnqN/nrJJdAtRvqn0e7u22JmlW/sEPxxsaasH+h3Zg7w7B1wuj/jNoiPgIaZpLONjZP+rTeYY3gvy0k98rtzk1FAVnMqA1t9wq47pYfR6Ir191iGw10zmL2DzzgtqkWs04gS91ycS4P2znJg1ig16QQmKz+lZ1DsfQdctvU2e/kd1eHL2VxKCiPidE6y+Gz9N9mC0T9ZED4HrCBVsiZYBc6HnYP+Q0oV3pt7Z4AgNMfDcbzvMnOPVFLD7+GZ4qmnQ+dnW47ISxGNdK5UmbR9OLhPmn+skh0pAkd6ArYgP6p1zwdzvFeqjn1dKOwMlTfiumuRZMovCtlKemz+sTW15zJCzpzoNjOGu10+2eRZPsc76rlHx67hnwhsMdJlv27pMNBUWOMgXUwxiIiE0VkkYgsasaWVIcpKWhLv6zbRH+ukg6Z9N3cZ82UNxnp1qxNdZiSIdm+0D8QkSEA4LYpp5IZY6YbY0YbY0ZXomuWt9vpSEu/rNvUYxQliaz6buLsPiUF2elWBqY6TMmQbF0ujwM4BzbD+BzYkHdJ0rLGDol6zg5Do21u23PW+pgz4vngvCOj9he7WLXd/NG+kaz6nrfs/bJ90ESy0O82BBdAzAK4DS4/fjKNgieHfNrGqE42L6Rrj5XHyNC6i+/pMjduCPWjH/X35oJcnAkw0w2pubgUxYTH3PJnAMCVN94ShHNczeoLqJb4Yq6X7nOmOQslZX50ln13O9p2PbReSmxTr/DBlo5yLy2un11vNxc3BQWNuH5J2D//YLulPPMunW0/w810nfnkFnBZGQdQbv87p3eO2iONzQC7YP00Osd9vxdRbvrtccuoxdW1TyA73W43wCZ3j4X1dltFBsp5rs8MD7IFh3w9ap+62Gb+JOTme28g1zMfTn3fF0m7PIgmnmIzUaYL5bPTfrS4rKQGKgdQHVxTVcb++huFawd4uEYAu+p8wTE2GLKvh55O2uKDsFN1BohII4CrYb+wh0XkXNh8rTOyfoKdnFfN8/gYa9GMLfiHeQKw3VL1mxMehJ10shnAbwHVbQ6ZDRvU8LrtBKhui45YV1dh6CP9zeFybMHu11Eqhu0Rta/6+5yofUQ3a/GM/mX4S73rjAU5ued8M+slO8TPDJEqA/gyo9564qpZ3gfMMwB50V0vj1t8ma2LQ0NzvLecgmjE1dbCXHHWwUHIhbrWuO0cGh1N3TW0veUU1B3iScfxLFwuJOWtdQ5QxVmQ12SlWwAQGWp8vnXQUdx4jE3wOEuLrVx/fnWK/T4u8q0g8k/fQIdxzr6fqDqVZKTLYw5/CgDwrITRJZa6vGnOSVn5a/pPOhb6dBjzfpxp2i4io01ilBw40YQSs/PEjhovNMFCv+PNEDSPRhZP/Zau4GZG8yLRGzjw6PLs534piLxVP4GCouBRvPsdzK0Noktptw+a7lcfZEfU2O3COjqQY8X+O+YgdLXbNpAsvb6rM0UVRVHKBH2hK4qilAk7VHGuQrP8x2H685e7htHka1vtcLP/65tbnVM8uHiUH8pzkoEfIjeQLG7ox7jrjaIg0GIatt7feqWbFbV+WMxZNzQV2qcUzyE3SzUderrbcjAqSs3mokYctPOfkwNLXge5qovO+vW6jHNB8Lxxfp64tEffvyioCc5x9r6suiBa5L8nWo1qA7kNfDCaqi2c+6Xbo/Zd4ubRj6LbuBnvWEkLJsfqLV+LRH8KwN/butLmHUgrZ9XY9h3C7o9nQ/OEGrudeRlaUUftpxroP65Y1hoSnecX66bfzWRaMNpPNeBrTqH2ft5NdXGQLXwbreHfmnfL9UmxPzPUQlcURSkT1EKPYcvJXwYAvHw6pc5RDv2Fl1wCAOj+vy+gdIizIDlI6C2AVIGtardtIJmzHhbzzDa2HnyKIwVKXanVynXBgmxuohzGKjeRcBNZ7WyNr1xhtxfMJ6Fft5GfnUcfPqCbLwsSsDNF/c8luYwuwz8ptsp9WiinrPmgNAed2VLz10+uvAEklOmdQs9RXQ8AmHdnCGr+K/5I5zlLeDGngPrvl/sLz1aMW6EpeV9HaEawVN0obHBt2O0mtXabE0bJTaNqwv6nXLB8IY1UNtS5RihShgoqjOar2SbMnHbpik23RaKf/yoU77pe9gEA1JqQTFD70xvpAr6SV1zKJ4+GOTU4jux1qha6oihKmaAvdEVRlDJBXS4xvHui/TvXS4Kb5ay3wxC1x1M217pwGfzp0IIwNK9M2gJhGFdNMh7q++E251b7oB3nyHaPadPwfbxdyLl5MB3WwkNI94wrg8ulcmZw4zTv5xaCXtdA5zzltqm6q5ezyyXXi0TzTFGvV9ZVXG46P8PGmP3evcJurDi3EbthnM4raAjfQj2xwn4XmxHchWvv3ZPO34DW+H7Qqnqiw3/eXOvUw7XmXZ+bT66M+dYv0hQVcgQwNwRATzvZ9s/ZY8nlMtcFVW+m1HiaHBvi+LVB1uQDoCFIvS0q/Ab4csHfRZifUnszz/Xw8wX49+LnVtUHUTeqh97kg+B8TvaLcquFriiKUiboC11RFKVMUJeLo1PvkDN89lftMOjT7SE748Pr9o7aXbe8WLgHSxuDMJz3w3au974yRhbnouDMDD8E5+XINsa064PofpelwoviVlFGS6NbiJiSNJoXk0thnS8qxe4gP80/1aK5/jnjunOu3ATscvF6jrtfXC48EO/O8OezS4W/k7hzqu2GKwyMJ7eCK9o1bv3MIOMsoui75Hx3Dz97Pt1XyXCteX9fLu3gv3cqDUN59rPH+JWTuEa+c2NdPoJknK3l3RpcCqPObUPqy01nXx12T7CbfZasonM4d9/fn7O+6u2mFy1NyN2mqcE16AcR9Zu4RbnbRi10RVGUMkEtdMeK2i9G7bluNZhTVoS/ql2fLEWrnOHAkrd2OLjiZQ0kiwvGsVXoreRUFprP8Y2rxU6yRrKcjnaWCBffSqjL5HP72Vr0Vv9Ykv1XimcqBM1JW6a9Asr8k4vLL2f8d8EWnxthHUGiGXVRc+ACW1Z27TcoELruTjq4xm25MJv/HGytZl/CNXN6IHxGrxN+Fv9dU/B9He2O4tE0qqiwKzuBFsvCIloDtdGPBDlxwFnECWWEqSCcz3MfxTPE+btJHiETp1O7ntobvJ45Tz37+RRqoSuKopQJ+kJXFEUpE3Zql8sn48O49ZUzw3TfN13e9KYbQ6CiK8Ii0aVJZwQ3hx+yxQW5NsbIgNaFvYAQQDsw5jgAE1yBLY6zTh7mGuzOoaAo10b3rOECRj4QxK4fX0aAp0yzuyM5WAmErp3vgF4yqe4X91PzbgUebrMbxgWWR1Ngz3fZ26lI2uIJUXPtbNeYX0/XOZPaHMTz+ADkOzH7CsEWBFeg33Iw0wdDKag5i4OmMaUuWpy+K6jvJaTg++Jw1M98AHUTHXYB5bZHq0Sxu4prp7vnPIHO8QXB6riwWD21fU46B0D5+pmhFrqiKEqZkM4SdHsA+COsGWEATDfG3Coi/WH/ZFbD/lk9wxjzcf4etfxoMpvxGl7EVjQBEAx1lqzqNldsADAT1uQSwFXIUv3mgk9gI9tet1sAqG6LTToulxYAPzHGvCwivQG8JCJ/hc3KfMYYc4OITIKtiXZFG9cpGSqG7g4AuPSqMITrKkEV45acDQAYOC+/mS0CwQgchD6yC1pMM17AM4CtGD4JGes2bhHjuDxozl5obyV7fyxF8n32ABCG/5z+6zMSJlFlO85IuN9tm7hwQjW1ff5695j9nNnCmTU+m4e7cyVshczjAQyBfeHcMEhEDkBR+m6cW8jDbhbK+a9wLgBeGm6ydel0WhOWcvz2bvdH7dmjnCthFNVYp0Wm4/OvfbuBZO0tCN0Jibr9D2Sv28/R2s3AncpX22TfHulssPvM1M86NX4GANh+A52yibN9JrgNZbl4V8u0kKN/mNkWtV+oPAatYdeP+73U029kjMuUo7x5m9Xj8a4z/l3msdqiMWa1MeZl194IW3RgKIBTgKi4wr1I7HZKGnSV7ugjuwAAKqQSPewLtgtUtzmiD+wLB3Dljz+H9t0c0RuJuq0AVLdFJ6OgqIhUAzgEwPMAdjPG+EjhGiRGdkoOqQgf9eC59q//v/QKgYo/bRwUtXe7yv6d216gZwOAz81n2GijNpsA7J25bjkPPbpqTDuV5eVvwdbiMLRiALV9yfJZtKDwKFvgqOr6FZGosTIEuAY2vwsAWHs+5UlzTvo6H1DiQKm3zOPy3YHwuStiZJ4NgDWNitx3+bm8dcjWMll8PghHRv1gY2cp3onzI9nY/Z8JB4x0WypBnxiEq0jaAsEyT5VD315xrg1+X5a65b7r+yfPnPSFq3heBY1AuBCcY/v4nrYxP4xesJKKny+3ueYjTl4SiVb0dgub14SFpV+g1He0+MQJGn0mzF52z95EgdK5Da7BSQLcj73Vz8W52pvLkJq0g6Ii0gvAbACXGmMS1kgyxhikKD4oIhNFZJGILGp2fjYlkRbTglewAPvadcES/o6kq1uglJbDKzW2AngYAFZl23dVv6nwuu0D1W3xSeuFLiKVsC/zPxljHnHiD0RkiNs/BClqPhpjphtjRhtjRlfSqj+KZbvZjlewAIOxJwZJ5D/NWLeJfjklsA32hXMgEBLXVL85gXUbjfxUt0UknSwXAXAXgGXGmN/Srsdh537f4LaP5eUJc8XB+0bNXw26r9Xu31/3L1G735IFBXkkYwxexyL0RG8Mc8tbOfKo21RFl5KXV+NjKXjKi+o6V0u3DWER6c8/tUNZOYsMs0mhufbbztXyVJChqZ7+49txi+amqted/LyAdRMYWFUOAHAkgL/4nSXSd73Oq4NovzDcP+wSuxDyCxIs2NUjTrJnfIuG6Jw37eOG9c+TkNterxyEiwt6theYS9ZtFNTMQrc8h8K5nyrIpeKLix1Npyyktu+TXEJi/h12240WOB8epvGbh0cDALp/Etyu6zfa/rXrQ6SPcZxn7pID+K3J5Qaiz8ABXa9HPo5dbH7hc/ZM+Zz0zIOj6fjQjwJwNoBXRcTHy6+E/cIeFpFzYWcknJHifCUFn2A91uBd9EJfLDTRhI++UN3miHdgJyMNglvd4AAROQmq3xywCom6XQ/VbfFp94VujHkOLok3hmNTyEuGzgdYy3fizNaGwgF3/3vUrr5vYav9+aafDMBxCVV7gPlm1ifGmPXIWLdcgjQ5wMQytg44+PJO0nF0PpW/nb7q7Kg98Qk70rm875WRbHlfF0gdTZfhSrg+I4wDRzwTtVuN219L+/3n4jK+H8XsT549OhQAlT/FNa8bY550/ylS361s3a7+ViTZf1kIsr05TNcjAAAHYUlEQVTrVsapMz8PpziD7p2zQv3cS1ddH7Wnfs0f20D3YeswLuAW1zfirHY+d08k6nY6jHk/S93yAtxuiFEf9k486lYAwKxt4bfy0RgqmjXJ6W9xmO2NG1zgclKYUXuY6Ru1mz+x26Z+IXjf/2cuksyDQx4ptNS6LQdCOXHA64y9TD7Z4jske4Tarpx0QtA087K5Hp0pqiiKUiboC11RFKVMKPviXMt/aCfujO3xaat9VfVbw39MaS35nDlx9dCTg4RAoquCx5ZuaNgr5DdH3iAKNnVGmDnnF93tcXK4z/73NtjG/HBYQkGudS6/vBsNZTko2uSDRHFBUX52LjLmg7bZ15HOP17/7AY7wW7qgmQszYa9SS4CAJxzzMORbEr9T2yDZn9u5iyRaJJjNd2HfV5tBdri5i0kP3M+6Isor/wCO2fhmKNC1Hz6ty+xjTmvh1P2C24q3OBmgNZQfvikegDAf5rg3vgK/jdqdxnsf+91kezPN7ri6ZQD4GecAsD2wd41yFk5nHLp3WCDSOb1OINkXOwuLmhagDx0RVEUpbTRF7qiKEqZUJYul6axh0XtZ8b+xrXKffJCXJZL3PA6Lt8ViDIceMmuOpvLW2fqI9E5q8Lw/9y5EwEAA7gq0gSXNXBpmO5fdQuVAZjphv8tVKc6oc55W+4iJiEZ2G3jptUXuh46P2tzTJuH41ZHg495K5LcdH7IHJljvmkbNELv7V1NF4Xv7u//XhMOaPFZHdl87jg9A/l3ZW1ClL4zzbranp32lXD3TTbJrtsF4QwZRS7Sy51O6mmaTP1lAIDrKDOqcS+qse49IOOrI9EQvG8bQYRv7vZ01J7n3YAVVA+ghUoLxGa5JGXvAEh8F/lidNeRzLtuMq+Lrha6oihKmVCWFvr7R3WO2ntWtLbMfSGuyk9DUHRHD4nGF+eKg61ytshcwHFmLclqAAATrgqz7SZMDSWH9zavAQAm3sgzb521PTWUIG2cenjr+7fMJhkHOOOKR3nLJ1VAt5SCoe19BzxCsvpf8/u9g2hGmGV4wJ02CHjxqzdGsttf+plrhZWHVozlClK+9DjnSqcL67GQr4ZOCIFXNz9h5IRob/ejW/86B98XRjVrLr/MtWhGbI211g801ZGosaEhaleeYPtk8wk1kexn+A/bWBr67rzvc/64C74m9N2DqO3L5rKF7j/XqzEywNUYQmK/ia2WkBZqoSuKopQJ+kJXFEUpE8rS5RLH9evDKiILvlkNADCrs1+MtTyIcw/wCixuaEjFn6o2hgDnVnSxDS7YNdUNQXmFFs5Jj1w+7D6JC3AycTnccUXGUgX1Sgl2eTn3wkW0gPDR46PmPvfa2uegMt5o8e4X+qxzOc/c5+yzHrMJkLaXhx4XiM6WbQjP7YqGLa2j/e4eNWGOxJru5KaK4Pxuq9t5chjJgs6ahzuX3YZQd3+BuKAo666ugc73rkHWB3duH4ClFb6i6Cvrid873gWXKpieGWqhK4qilAliCjhDso/0N4dLydfzKirzzayXbI3ozBDZ3QATc/AEbH3EWcZsffgAHluDviwrW90cOPIzQfmarWfx5odrstItkEv9xpFqZOFT3apJ5q23OKscCFZkodM1p8OY91MV8WuT3OmWA+VxBeq4nzrLvYJq8rZ4PXKV8LHU9tZ4MYLw6fVdtdAVRVHKBH2hK4qilAkFdbmIyFoAnwE8tXCHZwBy+3mGGWMGZnqS6jYtstItoPpNA9VtIkXpuwV9oQOAiCzK1o9ZipTS5ymlZ8kFpfZ5Su15OkopfZ5SepZcUKzPoy4XRVGUMkFf6IqiKGVCMV7o04twz3xSSp+nlJ4lF5Ta5ym15+kopfR5SulZckFRPk/BfeiKoihKflCXi6IoSplQ0Be6iJwgIv8nIitFZFIh750LRGQPEfm7iLwuIq+JyCVO3l9E/ioiK9x2lyI8m+o2f8+mus3v86l+c4UxpiD/AHQG8CaAvQF0AbAEwAGFun+OPsMQAIe6dm8Ab8AWQb4JwCQnnwTgxgI/l+pWdbvD6Vb1m/t/hbTQDwOw0hjzljFmK4CZAE4p4P07jDFmtTHmZdfeCGAZbIm1UwDc6w67F8CpBX401W3+UN3mF9VvDinkC30ogFX0/0aAFvzbwRCRagCHwC6TspsxZrXbtQaJy9IUAtVt/lDd5hfVbw7RoGgWiEgvALMBXGqMSSgVaOz4SlOHskR1mz9Ut/mlFPRbyBf6ewD2oP9XIdRa3WEQkUrYL+1PxphHnPgDERni9g9BRxYFzA7Vbf5Q3eYX1W8OKeQL/UUAI0RkLxHpAmAcgMcLeP8OIyIC4C4Ay4wxXDT5cQDnuPY5AB4r8KOpbvOH6ja/qH5zSYGjwSfBRoDfBPCLYkams3z+o2GHTa8AWOz+nQRgVwDPAFgBWwW/fxGeTXWrut3hdKv6ze0/nSmqKIpSJmhQVFEUpUzQF7qiKEqZoC90RVGUMkFf6IqiKGWCvtAVRVHKBH2hK4qilAn6QlcURSkT9IWuKIpSJvw/22YwQKSqCvEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This corresponds to the Dense linear layer.\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "\n",
    "    f, ax = plt.subplots(1, 4)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    \n",
    "    for i, modifier in enumerate([None, 'guided', 'relu']):\n",
    "        grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, \n",
    "                                   seed_input=x_test[idx], backprop_modifier=modifier)\n",
    "        if modifier is None:\n",
    "            modifier = 'vanilla'\n",
    "        ax[i+1].set_title(modifier)    \n",
    "        ax[i+1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Guided saliency seems to give the best results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## grad-CAM - vanilla, guided, rectified"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These should contain more detail since they use `Conv` or `Pooling` features that contain more spatial detail which is lost in `Dense` layers. The only additional detail compared to saliency is the `penultimate_layer_idx`. This specifies the pre-layer whose gradients should be used. See this paper for technical details: https://arxiv.org/pdf/1610.02391v1.pdf\n",
    "\n",
    "By default, if `penultimate_layer_idx` is not defined, it searches for the nearest pre layer. For our architecture, that would be the `MaxPooling2D` layer after all the `Conv` layers. Lets look at all the visualizations like before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VY2j2tCR6q8qPSl97fFpfs0c/NUJY3Vh9Y5y71mV0A+n4ejWAmJvqIO/aRSK+Kw25R+KgvXYNxmP1oOfKnP1l3wI2D7PQDcMwKoRGf59E5I/AQcAHzrmdgqwvcDt+Klw1cJRz7qOGrtEa7huRMhetCdFrm17S2CrniS7/40O/zlqbVlYf9gs/w3HqEJXKdI+0lM+o2721PvDINCvSrfm8GbVuOq+4KpbwPp3ozJfl60Cx9NtYOtpgWe6pRKFTc/rI32QiPVP0ql/9GIC5x+2azolW+6lJtHwLFfcYjfVqXQ8djhgt9LxQO50mtpFUqHQETgcewodAPgyU9t2tTTQJ1ajl8X7zw1NS71EPdt4wzs9yvp/D0zmxN1SVnn9lH7XIcnXevbV+qutsIel3qJI1tKJUZCJwP7AZ4MN/i6bbpibIygs7LINx3lLSFAt9GrU7hQCTgIedc8Px35RJBa7XRsMgtuKLjK0rNv0WhG8Df64rNN0WhAnUSq7vMd22MY026M65x6iff/MQ4MZQvhE4tMD12mjYRDajI/VSAJt+C8KXqe1YBUy3BWIsOflgTLdtTEuHBAY4594P5YXkZ1IqCEfNT8m8bt7aL+3S4ePUt1rbxOt0vu+5rDx/rc9x88rUhzPZjp2SKqqC+2XPHyS/Qb/fP9X0SreeIupXJ8XKiaPuk7ryXxjpB9DO56JM1vfWpPu9jn4SgH2npnzoyw8K7pUZ6j4vqmV4sj6wbgxUkrDYW8lNxKTrq10yMc5aP1uDOb6LpNtYN11xXcdoEw1NouDe+hG/y0S735p0td3RrwHw+MS9M9nKu4N75QGti+qc+ujB2dGp2CWUdXz2qjpboLauo37r+i/q+TOK2y401FrFeucl52ronAobDI20elDU+XSNDaZsFJETRaRKRKrWUElRI6VhffrVus1fxMBYH815d/OXdjMaolm6Xbe4hDWrbFraoC8SkYEAYftBQwc65651zo1yzo3qSOeGDjNq0yT9at3mp0M1cmjRu1s7t4zRAC3TbbvNGjrMaCYt7XjcAxwDTA7bvxWsRnWomjc0/bN1g4fx3k/3ysq7Hpam8f/7Tw1NdYfDHzs5K782/rp6+z9Oob618gKVgFbqt6kx2NolEKamPzAyk8z5l3eFPDsmddkPGJAig0as9i6BQzvflclunBB0+rROvvVuKhNdCvsk0fEpemWn67xrbG8ez2SP410Os69WS9lNUQ1sdUxUpZey0y6HWhTg3Y36bWzeuJ5yH+um3E9VPmHXi+N2y0S7b5n2Dwjt4V7dn8xkD44Pybee0C6lf6lyddiqyQPHJs/H8BtmAfAVpd/Hgn7nXqmila5X158dn023zx3IcbkUt11oKB96Uxd3LoabJe+ebejOaUrY4q34b18/EVkAXID/wP4iIj8E3gKOKmYlK5mX3TN8xGLWsJrH3d/B/3aYfgvCGcBzeHfUHmC6LSAn4H9IPsTnB2oPpts2p9EG3Tl3dAO7mrf0UAvp+YJy04Q1jZeMSu6Fvt38EjmPnTYlk/Vop845Pw18NpfJh96clX8zN81O7X+3j5Veu7j1vr+dZXSt/2e46Uucc0spuH6jxaVjirV58VbYPpNEF/u6nXn/ZZnoo33TAGm/4FcewjuZbLNj3gZg8Wy1cPEUnTQpWs7puTe77u2s/PKbX/KFi9QpYQrBSadckYmu7fCTtH9SsECX6UHRGuByaj/vkALpNm/AtWPOvrxYedUrCtlerzrrtEzUZ0ya9dkpjDnp2H8mBLd0lZrRe+8YdZ/YK0g9045T0j1f/yD0Bi5RpwT9fu8n12aim7qkmb5MDveq1mmOY482PuM4nHu7CO+toiELPG9Fo1JRZoOrNlPUMAyjQrAG3TAMo0Iosw5DfQbf/FpW3mOdn2o+6J40cOS29HHPi9elCKkeBfqZOrh7mrV88IVpevai83239v9M/o9MNvCm2UC55FKPA5L64+2VI+uaU1ayMAt/zu9TnPh/nPRfWXkv/GBdH7V8zM68BMA/T1d51TdXQc+z9/FbNWZ3HDekf6KHLI29Zl3t3/w5TTx876RBWfnemiN9YbIaNV8QP4difB55ibgCtQbudBh28BfqRYvDnKdZM1O+hatGJvfLqJCdS+c7//owv/rTg1MOSdfZTaVEmB3Kam732Zv+Iv1zZdjeoeoRIjIn19LvwKz8z5UH+cIVaqB7QdRBG61slEexc4flXb+p9yxRCgKz0A3DMCoE8fH/paGX9HWjpThjJssnJCtn5eHJahjcezkA925ftMhKAC770Kc1ffjEFD4pT81q9nVmuOkzfdxz8xDZxUFMZNarzrYB9GzBoWGr1gzNYjX17Hm9f7wP39t1q5TCOFrrnylLf7WafxCtzWEqTe4YUljefmGkcJsqlXL3zbBV46wPjU75b87ED9rO/pkOawzbmgVJxpAW6RZA5IsudRuCXvVaq9HyrrWSjirHyESd/Cxn9aYe26aB9pHdvV71mqLtww2WqkDaZeoDivrV5+yn1tocOzekz9U9oOX163bHmIOy8sS1UwH48FiVsOu2sK2JPaBxOPeCXsi0yUjHUY4+VY0f2NbkDb42ZqE3NaSyMZZIk95ds9ANwzAqBGvQDcMwKoSyHxRtKr1velqVk1w6+Ec8ZNNv1Dtn3RA1cKdcT+0W1I8vnzN5SFZ+dD8/sjSwfXIrnNnXL977zKVDM9mK87+YrvnoC409QunRA3Sxu32EkkVXwBIl0wv1hpzcsxamvnrHbX0XfNtNk0tlZ16uV9YDfVWknuRUTvL7R6VMS0eM8knA9+axTJbnZqg1nTe6O/ISNhUKrb+8++n90eVyRMqANXzwa9TlM7VS0Dv4d26FutAgfO4rHfu/l3JZ5en3DdKU5/OH7w9Ah+EprV2clauvqfXbqf3q+s8TW46NKd94S/KtlzhG3ix0wzCMCsEadMMwjAqhYlwuHbZII/Cf7JJilGMe9LWLchK/5cnIz7G+3XHp2O8feAYA37j0kUwWXS63D3sgk33rom9m5dXjGq574YnJo3QE02d1tsCSnAyC26bil0f4POc6znye6r7P/UdI5jRN3bmDjwCZMz7Frn90SOq+v4f/bFaQppHPekaFV0wNW7Xu8aOH+qDqLoemFMFra9Kru+buEHVyr3qOYrpaIgtzZPq+uoseg21WpYifrUMiLR2RskT5jf6Bd4/M/9uOmez54NrZfP/5mUzrcmnICqllM1TQ/6yH96xdH8jcQZvtmlIwLH4rxaFzW5je/7Q6J8/9sKHTWMTKyhxZY0s7xmvqSLGGkowVALPQDcMwKoQN3kJf9v0vA3DGz2/LZOO7JfPjwPPPBmCTaYVbcSha/Y8+kwZKB/7Lzyo9umdK4Tpl6J1Z+ZijzwKg163azCkW8Wdf90AamTn5arDWq5Oo5wg/sKYH3fqrFLVzV9W30FkVrv90ioFf+Oo2qdxvm3r3UWHSygp8M8mCBb6qwZzksSeiZy1+lndggQhJwFbq5Fs5PaCFatD9iRCivVMK1V40zM8k1amC26v+4eJZIfD+PHWb0CtYeGzS6U0TUrnd5p8AsG5e93TOI+r8qOvZShYsz8U60D8vlrqWNdrUFM0bEI1Zy3FQWPdOanIStelWtUv93cUcSDYL3TAMo0KwBt0wDKNC2OBdLp/39F1Y7Wbp3S71cx7/9VUA7L/oR5ms8/1pwejWsHZpGqSbdqpPlnTEtGsy2dYdUj2Gn+YHvhbdWpBbN8KaOtu65Yhyv8wO7ozpSfTgFv6ZFu2YkkxVrx6aDrg+bFfdrq4ZVieqmphEXVRSp9ht1QOKugsbL1+tl6d6JGxVrvZa/daYj0AlqcoGBRtcLLoVxHtrt04saz0rl9eLQYd3J9GsoX6A8tP903yGZWySDpgctrMfUtcMn9lN30oi9S1e1yO4WrR+9UBtvzpbgCXxu3O/Emr97hy2Wr86sdsGSF4cfd40fT2YGQMGdlIylbYhu6YecH4xbF9VMjXgn7lktGumFS4Zs9ANwzAqhKYsQTcE+BMwAD/6dK1z7koR6QvcjrepqoGjnHMfNXQdoz6r3Ke8wnN8zipAGBwWTTXdFor3gJ/ip7oKQH8w/RaGBcBEfC9EiAPSptu2pSkulxrgLOfc8yLSE5gpIg8BxwIPO+cmi8gkYBJwTvGqmk//q30ExpiBZ2ey2cel3OXtYiekyH2Rxbv5+OL2kp9w7vFXfXd1O1JmQkEYzi70kk2ocWt41icD74LXZQF0u76l0uqwMnTlp6kMjSEBXnQNALW7k1Xxn2olDP3SPsrNkpfBUb95en/s1uou6oX7hNssVUK98HSsc18l64h3u5yPdxmsBL7QX0R2oCjvbnRBaP3qhwyRMQ8ovQS3yNxpu9aTAfBIfN5qJQxLy+muvs76GPU7VMnU3AK2CP6tKtXHPy9cbLa+qF5wOz6bXoJuNT6l5fb4xnwYxdNtEchr+aIrRLs8tEpCWozNT0lzAHZRaS0+DWkbnlyUMq6uuyK4wPT7rF2M68ux3gLXS6PNnHPufefc86G8Ar9s+WDgEODGcNiNwKHNv/3GTWfpSi/xPtMO0pFu/gvTCdNtgRhA8v/2AO/otne3IAwEYq6inuBTJJtu25hmDYqKyFD8p/gMMMA5937YtRD/7Wkzhl3xelb+3le/lpX/PNQPKE28LI32/fJYn+t5q8nrMpmb+UqT7/X2Bf4X+IQj06zQCb39Sj7tcgNPG+cz9wkrvImwEtim8LqNlqOyEGsN4AVrsKY6iV4MVvuLevBPW6Bb+U0/ZYCFsdAek1KCs727pzjrTcN9+pB64SNIn90g3gPghdG7ZbKLx/7aFyaogcCndTy9ttwjdQeB3wH/8AV8d5szMBjNLWX5ZvptaFWloWGjFmw+1W82PytZieNJC6H3C5nUeqiY/C1V0q0of3zwVzLZNT3O9IVjVQK7Bborlter0/p9izAoXHbtQi0rt8l5zNWz9UnP3u4IH+N/Gv+dyYaq+RJP4tuFqi4jM9mqGjUfoAQ02REhIj2AO4HTnXO13kDnV8nIXSlDRE4UkSoRqVoTVjE3alPjaniJpxjh52Cv0/uaqlv4MO8QA4BPwGdxfKel727+j4bh7Y/vAYNpsW7X1c9uarSMJjXoItIR35jf7Jz7axAvEpGBYf9Aak9LzHDOXeucG+WcG9VRrVxjeNa5dbzEU2zOlvSXLB9Ns3Vb239sJNYAJxJ6/tFL2gL9NjRLdWNmDb4xPwoV39d83bbbrBSV3ShoSpSLAH8A5jjnLlO77gGOwUfLHgMUd423Rli7JFlQHx+UYnnvfNqPEu2r4tS/tdc0ANb8LU2zXpObkiufbjIzR1rf1TJpYVoSbYfzfC9U9wCdc/ybKrrTk61kO31qiXSb15XWr0QceKxWsjGpOMFH5ez+5ycy0WX4FAfjHn02HaeXO4tfb60I3XHr7TeHH5Ziorcd9wYAp85Ig90rj1WNwPRY5zRA5d0hDvgVPn76xFAGiqrfhgZFI9pVUR22c5RM6Xei/xHZ95qUdWwyPwNgj3+quftJ/fn61XnMQyj5+JOSm2bZfr4xvvXiH6TjLlajgfOi4V13oPTHwAi8Hyhbdbqs2oVa5LlccgceVW+3S/IY7TDAzyWJi3dD7bzxMZnaqsnKuIpe2YZi2wucV74pPvQx+J/hl0Ukhsmfi//A/iIiP8Q70Y4qTJU2HpazlIW8TQ9687TLJo/0xnRbIF7Adyy3B/9l20FEDsT0WwCexc9C2xEYC8zFdNv2NNqgO+eeIATx5lCcFZ9bydqP0oDbDSP8wN1vTj86k211mB9QOnVwslK+2rV1+UBPfdcvWvzwo2kwb8TVKbSu5t23653TR/oxvtYSQTDDTV/unFtK0XT7qSrrAdIY+qcH+qK5pwdFlQUZkkbdzIRMtP133wJgppoRqw30aOvp5at1VN34MIbUbXmSHbPlXwCo3npoJrtw4qXpgBnhOZZp67cDPsLlHSUb8m/nXFxJuwD6bWjELZL3tembU9bjhmlArctkbynetfbwTNZrP/+MjyilPq/OjvrVd1GfGCPDP5sNTNNHv32wn+n74jHp3Z0zL6U/Zkr4tFbpcYTd8bqNn+Q4nHuhgLotMuu1iPPs/iPQAAAGVUlEQVSbxdV0AlIKaIDH2Tsrz70yhJ9O1meF75sO49UWeqyHns3bivn7NlPUMAyjQrAG3TAMo0LY4JNzNZXNr0g5vVdf4bdXbn1gJrusTxo5eu0k3+8f8Hj6vVuieqC95vmudH8VCy2v+XjUYZ+mvOvltX5uY/mr46ugXS796+wDOig3QvBS6VWMth/jXS4j1fjkUDXm1zFcqlfqtaLTcGezRtXk1DXBf7CpCh3sPTZNqVx+UJgqedNYdSEdR10K8j5t/fWSOltIya6UyyV5PRjQ27u8VuvosEH+c/xCA3eJQ7JfUKf02lkdEPWqgnZi7L/Oyz5ngnrhq8P2bpUwbWV8n4qZd77ANJaIK0M5rFQirbhC16/3PzfJXlGzfLOpLvrd087FgK1YZBiGYTSGNeiGYRgVwkbjcsmj5s23cuXbTawv631zfZlroFyexM54QznS8/p+sV/eNf+waX5z8uVTM9HLp/wOgANP+XsmG6IiTZaEIf6XVKTA58qlEJdg+0zdc16Ig4lTqwHad1DzBvYJ22pVtydiHHVbul60O6Jb3QPJuuNdVLdcJdp6a6b3P10w8peZ7LRbfH7/7c9M7+6A99Qlg/fGqdTlH/ZNcySirpcqn0t1SDHQSU0I2GZESoUx/9CwSLXO4/1AeJ9qytzl0lALt77c5zXKLbZE7Z/iN3Nv2jV/f3UsqBj+DnW2kL+AeYFaYrPQDcMwKoSN2kLfOGloBZ9oaeVNp8sZ2AEIExgXrErm4LkHXQ7ApeNTwq7+ndMMw7giz9JFyULs1iPFxg/s7s3Nbsq6jbPx3lmUFuVe96JKehTHR0v2Nq83s1MDstgbUvqPhrOOS9bTIcLqRtdwZiZ6fKSPex49Kq3epAeLo+W9SA20tlf1GBDmFmhrPH4mb6jB7XeWJl3nWpQbOnkfV15ePf3sM3L2a2Lq4i1y9tVaWLqR67QCs9ANwzAqBGvQDcMwKgRzuRiBvIWlo3uggbzf0dXxtJKFgbPlVWl0b3k/NdIXu5uqC7qyT3KfzO0Xkm7p7m8cjJunZLNzynpVGBrKMV4IWtJnzpkHsCroVw82Vqty/HYqXc2e5xO+zd4pJX7ruHl61jWrOoVz0kBzO+XS6tPP36x9+zSovGyp9/msma1ca/ozfSRsq5SspvzDAApOXiKtxlrQEk9GMQvdMAyjQjAL3Wg9esAnWpvVOTLID+PSVkxejrQYGqYtdG0tVkfrNy9EsaFB4GLR0IPlxcmFeq9SIY1aV7Gs1xnVOohXWags65yBvXVdUg/ow2WhrPUcr/+ikumUvNFaX6at8hVUHI1N9u2Tsz+P1uX5axVmoRuGYVQI1qAbhmFUCOKX/SvRzUQW4xd4XNLYsRsQ/Sjs82zlnGv2mlym2ybRIt2C6bcJmG5r0ybvbkkbdAARqfJrNFYG5fQ85VSXQlBuz1Nu9Wkt5fQ85VSXQtBWz2MuF8MwjArBGnTDMIwKoS0a9Gvb4J7FpJyep5zqUgjK7XnKrT6tpZyep5zqUgja5HlK7kM3DMMwioO5XAzDMCqEkjboInKAiLwmIvNEZFIp710IRGSIiPyviPxbRF4RkZ8EeV8ReUhE5obtJm1QN9Nt8epmui1u/Uy/hcI5V5I/oD3wBrAN0AmYBexQqvsX6BkGAruHck/gdWAH4D+BSUE+Cbi0xPUy3ZpuNzjdmn4L/1dKC/1LwDzn3Hzn3OfAbcAhJbx/q3HOve+cez6UVwBzgMH457gxHHYjcGiJq2a6LR6m2+Ji+i0gpWzQB4NaXNJnUhpcwvsXFBEZCnwReAYY4Jx7P+xaCGq5mNJgui0eptviYvotIDYo2gJEpAdwJ3C6c65W4m3n+1cWOtRCTLfFw3RbXMpBv6Vs0N8F1EKFbBFkGxQi0hH/od3snPtrEC8SkYFh/0AICzeWDtNt8TDdFhfTbwEpZYP+HDBcRLYWkU7Ad4B7Snj/ViMiAvwBmOOcu0ztugc4JpSPAf5W4qqZbouH6ba4mH4LSYlHgw/EjwC/Afy8LUemW1j/sfhu00v45QBeDM+0KfAwMBe/NnjfNqib6dZ0u8Hp1vRb2D+bKWoYhlEh2KCoYRhGhWANumEYRoVgDbphGEaFYA26YRhGhWANumEYRoVgDbphGEaFYA26YRhGhWANumEYRoXw/wFaoOgTwbuUWwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vis.visualization import visualize_cam\n",
    "\n",
    "# This corresponds to the Dense linear layer.\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "\n",
    "    f, ax = plt.subplots(1, 4)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    \n",
    "    for i, modifier in enumerate([None, 'guided', 'relu']):\n",
    "        grads = visualize_cam(model, layer_idx, filter_indices=class_idx, \n",
    "                              seed_input=x_test[idx], backprop_modifier=modifier)        \n",
    "        if modifier is None:\n",
    "            modifier = 'vanilla'\n",
    "        ax[i+1].set_title(modifier)    \n",
    "        ax[i+1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case it appears that saliency is better than grad-CAM as penultimate `MaxPooling2D` layer has `(12, 12)` spatial resolution which is relatively large as compared to input of `(28, 28)`. Is is likely that the conv layer hasnt captured enough high level information and most of that is likely within `dense_4` layer. \n",
    "\n",
    "Here is the model summary for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_1 (Conv2D)            (None, 26, 26, 32)        320       \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (None, 24, 24, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 12, 12, 64)        0         \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (None, 9216)              0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 128)               1179776   \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "preds (Dense)                (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 1,199,882\n",
      "Trainable params: 1,199,882\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization without swapping softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As alluded at the beginning of the tutorial, we want to compare and see what happens if we didnt swap out softmax for linear activation. Lets try this with guided saliency which gave us the best results so far."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mSOgAkAlGuVRkxwfFlSRffvfQsOwZ6/oKsanffKkQ2959tdAYV3EUQ+rrlRr9EikzvT06XmokR7TJxppE2XGFyLJXpoYl3zgyaPMPPxOUTI1ciV43NWokGiFS5v2qomz0npeZ+t/NchFFXKEDQCZI6ACQCRI6AGSChA4AmaBTtCIedIq+Uuz7lCTtpdcKMTpAe52p/a9Tmd3qy6y3HXXclZkKH27MJE2ZWYx9Jl4mYIP2KgZHzyjG3k9USyuDWF3ri5d5fqps1LlcZpmA1Osy9R8AhjUSOgBkgoQOAJloZ5PoSWb2uJm9bGYvmdmVrfj1ZrbOzF5o/Tu3/uoC1aFtIzft9OJsk3S1uy8zs30kPW9mi1t/+7a731Rf9YBa0baRlXY2iV4vaX3r8VYzW6n06vRAz6i2bW9XcUp/mREmZaaAp7620SiKM0q8xvi4aLRBxWfGxGVXBPE1q4KCUUySNgex1NT/oWBo1a3UPXQzmyzpeEkfLc5whZm9aGa3m9n+FdcNaAxtGzloO6Gb2VhJ90i6yt23SLpF0qclTVP/Vc63Es+bbWZLzWzphyqO1QYGWxVtW3qnsfoCKW0ldDMbqf4Gf4e73ytJ7r7R3be7+w5Jt0maHj3X3ee5e5+7943UqKrqDVSiqrYt7d1cpYGEdka5mKT5kla6+9wB8QkDil0oaUX11QPqQ9tGbtoZ5XKypC9KWm5mL7Ri10m62MymqX8h6DWSLqulhkB9am7bqQ6zVGdppMwU8OjrHK1FnqpDYor9k9H67al6pabp1yHqSO52OYDe1s4olyfVv1DFzhZVXx2gObRt5IaZogCQCRI6AGSChA4AmSChA0Am2OACqISr/REW0UiQukaHJDat6HoH+tQmDu0ua1DFaJThPaIlwhU6AGSChA4AmSChA0AmSOgAkAlz9+YOZvZf0i+2vD9Q0puNHbw5nNfgOdzdDxqMAw9o273wPnUq13PrhfNqq203mtA/dmCzpf2r1OWF8xrecn6fcj23nM6LWy4AkAkSOgBkYjAT+rxBPHadOK/hLef3Kddzy+a8Bu0eOgCgWtxyAYBMNJ7QzexsM3vFzFab2Zymj1+l1o7wm8xsxYDYODNbbGarWj97bsd4M5tkZo+b2ctm9pKZXdmK9/y51SmXtk277r1z+0ijCd3MRkj6nqRzJB2t/q2+jm6yDhVbIOnsnWJzJD3q7lMlPdr6vddsk3S1ux8t6SRJv9/6nHI4t1pk1rYXiHbdk5q+Qp8uabW7v+ruP5d0l6TzG65DZdz9CUmbdwqfL2lh6/FCSRc0WqkKuPt6d1/WerxV0kpJE5XBudUom7ZNu+69c/tI0wl9oqTXB/y+thXLyXh3X996vEHS+MGsTLfMbLKk49W/23BW51ax3Nt2Vp99ru2aTtEaef8Qop4dRmRmYyXdI+kqd//YFva9fm7oXK9/9jm366YT+jpJkwb8flgrlpONZjZBklo/UzsMDGlmNlL9jf4Od7+3Fc7i3GqSe9vO4rPPvV03ndCfkzTVzI4ws70kXSTpwYbrULcHJV3SenyJpAcGsS4dMTOTNF/SSnefO+BPPX9uNcq9bff8Zz8c2nXjE4vM7FxJ35E0QtLt7v7njVagQmZ2p6SZ6l+tbaOkb0i6X9Ldkn5J/avvzXL3nTuYhjQzO0XSTyQtl7SjFb5O/fcbe/rc6pRL26Zd9965fYSZogCQCTpFASATJHQAyAQJHQAyQUIHgEyQ0AEgEyR0AMgECR0AMkFCB4BM/B9tMUFiXBCPxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YRZFctpQ9tlUBmyHCDnyIbEmwi81SiRwYcTWJxZq1kh3eETvRJTKLiNpXRG7l6R26iEgiVNBFRBKhgi4ikojjFnQzG2Fmz5vZejN7w8xuyscHmtkSM9uY/zqg8s0VyY76tqSmkEHRNgC3uvtqM+sH4DUzW4LcjsbL3H2Wmc0EMBPADyrXVDmmyLbnJxTxn7AuOACaYd82hC8nNvgJ8MHS2BLwpUXkDgxDbS9FcpnYAF8TicUGfJn3isglg8DjB9HMpkvD9g4ZxPeK3/IPZHB4e6wNbBCYPQcA/10Uk5ut477a3X2bu6/Of78fwAbkdoafDGB+Pm0++JizSN1S35bUFPUZupmNAnAugFUAhrj7tvxfbUd0bpFI/VPflhQUXNDNrC+ARQBudvfP/F/H3R2RSZ1mNt3MWsys5TAOldVYkUrIom8DB6rQUpFjK6igm1kTch1+obs/kQ/vMLOh+b8fCmAnu627z3H3ZndvbkL2W8yKlCOrvs0PwxSprkJmuRiAuQA2uPvsTn/1NICp+e+nAlicffNEKkd9W1JTyCyXiwDcAOB1MzsyDeI2ALMAPG5m05Abxr62Mk2UgkRWMXego7rtaCwZ9u0OhDM/YrMdmCxy2bp3PuujuFkq5RpGYmwmCYCzC38eunUPr3fvRyfy5O1sBg87PATgh1bESiW7jsrPZok5bkF395WITorDxGybI1I96tuSGq0UFRFJhAq6iEgiVNBFRBKh/dAT0dGr8MHP99u1HiB7jnBQspj90IsR2/S7HvbmZoOabH/x8/jNW0nswCKa2rvvBUFszwI2AAvw/ebpbFQA7GwBsq1C7hEj8drQO3QRkUSooIuIJEIFXUQkESroIiKJUEEXEUmEZrkkYsGk+2l8w6fh7Jcp875Pc0/B7zNtU9fiKHzJdzWX3cew2ShZLFln98Fm9VzFb84m8Jz+5zR1zyskOCvSLDobJfZ7YLNyYjNiKvU8lkbv0EVEEqGCLiKSCBV0EZFEqKCLiCRCg6KJuOvdb9D4R/8RLoU+ZZEGP9NUzJ7qlcKWyO8PQ30juxYfWBvG2r7McyeQWNtsEgSAs0gstlc8G8SNbddArq2G9A5dRCQRKugiIolQQRcRSUQhh0SPMLPnzWy9mb1hZjfl43ea2VYzW5P/c2XlmyuSHfVtSU0hg6JtAG5199Vm1g/Aa2a2JP93P3f3n1aueSIVpb4tSSnkkOhtALblv99vZhvAj/GWWprITzDvEz3ZXNLr22zJeWzmSzWXp5MZIgfmRXLJEv1WNkMFwOnk2jZdE7nfF0gs9hywGS31dZBFTFGfoZvZKADnAliVD80ws7Vm9pCZDci4bSJVo74tKSi4oJtZXwCLANzs7vsA3AfgNABjkXuX87PI7aabWYuZtRyGjj6T+pNF3wY+rlp7RWIKKuhm1oRch1/o7k8AgLvvcPd2d+8A8CCAcey27j7H3ZvdvbkJPbNqt0gmsurbQO/qNVokopBZLgZgLoAN7j67U3xop7RrAKzLvnkilaO+LakpZJbLRQBuAPC6ma3Jx24DMMXMxiK3EXQrgO9UpIUildMF+nZs4K+YbQKKGUAtdPAwdp9sQ/RWnrqJPdYqEgP4Ev1iBkVjS/8Zdg3HerzsFDLLZSUAtvHCM9k3R6R61LclNVopKiKSCBV0EZFEqKCLiCRCBV1EJBE64EKkS6rdyfQ5n0TibPbNwiLuN4utDmJtq396hy4ikggVdBGRRKigi4gkQgVdRCQR5u7VezCz9wG8l/9xMIBdVXvw6tF11c5Idz+pFg/cqW83wvNUqlSvrRGuq6C+XdWC/pkHNmvJ7VKXFl1X15by85TqtaV0XfrIRUQkESroIiKJqGVBn1PDx64kXVfXlvLzlOq1JXNdNfsMXUREsqWPXEREElH1gm5mk8zsLTPbZGYzq/34WcqfCL/TzNZ1ig00syVmtjH/teFOjDezEWb2vJmtN7M3zOymfLzhr62SUunb6teNd21HVLWgm1k3APcCuALAGOSO+hpTzTZkbB6ASUfFZgJY5u6jASzL/9xo2gDc6u5jAFwA4O/yv6cUrq0iEuvb86B+3ZCq/Q59HIBN7v6Ou38K4DEAk6vchsy4+wqEhyhOBjA///18AFdXtVEZcPdt7r46//1+ABsADEMC11ZByfRt9evGu7Yjql3QhwHY3OnnLflYSoa4+7b899sBDKllY8plZqMAnIvc6btJXVvGUu/bSf3uU+3XGhStIM9NIWrYaURm1hfAIgA3u/u+zn/X6NcmpWv0333K/braBX0rgBGdfh6ej6Vkh5kNBYD81501bk9JzKwJuU6/0N2fyIeTuLYKSb1vJ/G7T71fV7ugvwpgtJmdamY9AFwH4Okqt6HSngYwNf/9VACLa9iWkpiZAZgLYIO7z+70Vw1/bRWUet9u+N99V+jXVV9YZGZXArgbQDcAD7n7v1S1ARkys0cBTEBut7YdAO4A8BSAxwGcgtzue9e6+9EDTHXNzMYDeBHA6wA68uHbkPu8saGvrZJS6dvq1413bUdopaiISCI0KCoikggVdBGRRKigi4gkQgVdRCQRKugiIolQQRcRSYQKuohIIlTQRUQS8f/px8IR8CYwBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IJnQiokAwoRMRBYIJnYgoEEGMcnl/lbvt47gTih/N4nPn+8c4se7PDjDLrj7fnbrf67BDzbLnj3RHuVx98K1GSd+mB675O+3doD7zSqsT4wYX1SjONPRau6i14cNjvt+DOW5owlS76Awr6Jn6j21GLMaokQVGzB0AFrF+P1Z6ylojWqxlFfKNd+hERIFgQiciCgQTOhFRIDpN6CIyTESeFZHlIrJMRC6L4gNFZJ6ItET/ug+yiaoY2zaFRlT33XkoIoMBDFbVRSLSD8ArACYDmApgs6rOEJHpAA5Q1Sv3daz+MlDHyxnp1LwTLT83dioHMG+iu254bQ97anF3cf/e7VFr5fNsWR2gt5xv74zevnhFuatTNRp1PrbqZim2fJptW+RQBeoT1N7XAW51ig7xlD3eDY0cZRe1hkOseNNzXOv3o5+nrNXRaHVUbvW8frQR863/bi2L4HsfrTr4OqKrUQNU3+60bXd6h66q61V1UfT1NhTe3SEAJuGTrvI5KPwiEOUG2zaFJtYzdBGpBXAcgEYAg1R1ffSjDQDcrYCIcoJtm0JQdEIXkb4AHgBwuap+6v+XtPDcxnx2IyL1ItIkIk278VGiyhKVQxptG/Bsk0aUoaISuojUoNDg71HVB6PwxugZ5MfPIjdZr1XVBlWtU9W6GtiTX4gqJa22bT9nJspWMaNcBMBMAM2qenOHHz0KYEr09RQAj6RfPaLyYdum0BQzyuUUAC8AWIJPNre/CoVnjfcBOAzAGgAXqOo+5/hmOcrFp/uoEU5s1T/aj0h3DXLnUk8d/1LyOog7UmaPun9b7376NPP1o25we+z3vPNO4nrlXQmjXFJr2/FGucTZVd4a0eIbyWENXbFGggCANQrMHhlm842Isa7Nqu8Sz+utTV18o3oOLPL1QJ43rSgobpRLp2u5qOqLAHwHqmx2JkqAbZtCw5miRESBYEInIgoEEzoRUSCCWA89jj0tq51Y7Q/cmM8f0DPN6uzTCCw041zPPO+sKee+jlJrivxAT1nrGMZyAN5jNHrKWp2avqn/1hR767i+6z3ciPnWLbc6QMvV+emrb3UtH8A7dCKiQDChExEFggmdiCgQTOhERIFgQiciCkSXG+VCVJ18oyWsURu+UR/WSAzfiBjruL5Vgq0RLb46WNP0rU0rfBtcxNmQJc5ooaSjUXypkqNciIioDJjQiYgCwYRORBQIJnQiokCwU5SoKsTpzHPX6ffzrYduxVs9Za0OUF8drJRilU2jM9F6z+Ic17eufJz3N2kd0sU7dCKiQDChExEFggmdiCgQxWwSPUxEnhWR5SKyTEQui+LXiMg6EXkt+u+c8leXKD1s2xSaYjpF2wBcoaqLRKQfgFdEZF70s1tU9cbyVY+orNi2KSjFbBK9HsD66OttItIM/zbcRLlRXW07zsgIX1kr7hvJYcXjjO7wvU1xlipIKulokjgjdcp1DemK9QxdRGoBHIdPtiCZJiKLRWSWiByQct2IMsO2TSEoOqGLSF8ADwC4XFW3ArgdwBEAxqJwl3OT53X1ItIkIk278VEKVSZKVxptG9iRWX2JfIpK6CJSg0KDv0dVHwQAVd2oqntUtR3ArwCMs16rqg2qWqeqdTXolVa9iVKRVtsG+mRXaSKPYka5CICZAJpV9eYO8cEdip0HYGn61SMqH7ZtCk0xo1xOBvAPAJaIyGtR7CoAF4nIWACKwpzhb5alhkTl0wXatq8zL2knX6snbk2Fr67p8Z9Io3M5Tkdy+a+5mFEuLwIQ40dPpF8douywbVNoOFOUiCgQTOhERIFgQiciCgQTOhFRILjBBRGlqBpGr5RDgFP/iYioejGhExEFggmdiCgQTOhERIEQVc3uZCLvAFgTfXsQgHczO3l2eF2Vc7iqHlyJE3do23l4n0oV6rXl4bqKatuZJvRPnVikqbBKXVh4XV1byO9TqNcW0nXxkQsRUSCY0ImIAlHJhN5QwXOXE6+rawv5fQr12oK5roo9QycionTxkQsRUSAyT+gicpaIvCEiK0VketbnT1O0I/wmEVnaITZQROaJSEv0b+52jBeRYSLyrIgsF5FlInJZFM/9tZVTKG2b7Tp/1/axTBO6iHQH8HMAZwMYg8JWX2OyrEPKZgM4a6/YdADzVXUUgPnR93nTBuAKVR0D4EQA/xp9TiFcW1kE1rZng+06l7K+Qx8HYKWqrlbVXQDmApiUcR1So6rPA9i8V3gSgDnR13MATM60UilQ1fWquij6ehuAZgBDEMC1lVEwbZvtOn/X9rGsE/oQAG91+H5tFAvJIFVdH329AcCgSlYmKRGpBXAcgEYEdm0pC71tB/XZh9qu2SlaRloYQpTbYUQi0hfAAwAuV9WtHX+W92uj0uX9sw+5XWed0NcBGNbh+6FRLCQbRWQwAET/bqpwfUoiIjUoNPp7VPXBKBzEtZVJ6G07iM8+9HaddUJ/GcAoERkuIj0BfA3AoxnXodweBTAl+noKgEcqWJeSiIgAmAmgWVVv7vCj3F9bGYXetnP/2XeFdp35xCIROQfATwF0BzBLVa/PtAIpEpF7AZyOwmptGwFcDeBhAPcBOAyF1fcuUNW9O5iqmoicAuAFAEsAtEfhq1B43pjrayunUNo223X+ru1jnClKRBQIdooSEQWCCZ2IKBBM6EREgWBCJyIKBBM6EVEgmNCJiALBhE5EFAgmdCKiQPwfiQUQAGYdIJMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Swap linear back with softmax\n",
    "model.layers[layer_idx].activation = activations.softmax\n",
    "model = utils.apply_modifications(model)\n",
    "\n",
    "for class_idx in np.arange(10):    \n",
    "    indices = np.where(y_test[:, class_idx] == 1.)[0]\n",
    "    idx = indices[0]\n",
    "    \n",
    "    grads = visualize_saliency(model, layer_idx, filter_indices=class_idx, \n",
    "                               seed_input=x_test[idx], backprop_modifier='guided')\n",
    "\n",
    "    f, ax = plt.subplots(1, 2)\n",
    "    ax[0].imshow(x_test[idx][..., 0])\n",
    "    ax[1].imshow(grads, cmap='jet')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It does not work as well! \n",
    "\n",
    "It does not work! The reason is that maximizing an output node can be done by minimizing other outputs. Softmax is weird that way. It is the only activation that depends on other node output(s) in the layer."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
